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Analytical and numerical inversion of the Laplace-Carson transform by a differential method. (English) Zbl 0998.65127
Summary: A differential method is presented for recovering a function from its Laplace-Carson transform \(p\widehat f(p)\) given as continuous or discrete data on a finite interval. The introduction of the variable \(u=1/p\) converts this transform into a Mellin convolution, with a transformed kernel involving the gamma function \(\Gamma\). The truncation of the infinite product representation of \(1/\Gamma\) leads to an approximate differential expression for the solution. The algorithm is applied to selected analytical and numerical test problems; discrete and noisy data are differentiated with the aid of Tikhonov’s regularization. For the inversion of a Laplace transform, the present formula is proved to be equivalent to the Post-Widder expression.

65R10 Numerical methods for integral transforms
44A10 Laplace transform
65R32 Numerical methods for inverse problems for integral equations
Full Text: DOI
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